New answers tagged order-theory
3
votes
Accepted
Posets of equational theories of "bad quotients"
Let $\mathbb{R}=(\{\textrm{real numbers}\};0,1,+,\times)$. Is there an equivalence relation $E$ on $\mathbb{R}$ such that $\mathbb{P}_\mathbb{R}(E)$ is not upwards-directed?
I will assume that the ...
- 11.9k
3
votes
Accepted
Sizes of linearly ordered subalgebras of powers
Yes, and you can find them included in your infinite linear subpower. The variety $V$ generated by a finite algebra $\mathcal A$ (which includes all subpowers) is locally finite, i.e., finitely ...
- 43k
1
vote
Accepted
Large Borel antichains in the Cantor cube?
The answer to the More Precise Question is yes. Define
$$B_n=\{f\in 2^\omega:f(i)\neq f(2^n+i)\text{ for all }0\leq i<2^n\}$$
$$C_n= \{f\in 2^\omega:f(i)= f(2^n+i)=0\text{ for some }0\leq i<2^n\}...
- 400
2
votes
Does strong stochastic ordering exist?
First, for the discrete topology, $U := \{\mu\}$ and $V := \{\nu\}$ are open and have the property wanted. Surely this is excluded. For the weak convergence topology, the Wasserstein metric and the ...
- 1,931
2
votes
Accepted
Does strong stochastic ordering exist?
You could define a distance on probability measures by the smallest $c$ such that there exists a coupling giving mass $1$ to a $c$-neighbourhood of the diagonal. Many pairs would be infinite distance ...
- 8,464
Top 50 recent answers are included